How do you graph 3x + 2y = 2 by plotting points?

To graph the equation \(3x + 2y = 2\) by plotting points, follow these steps:

Step 1: Find Points on the Line

Start by choosing values for \(x\) and solving for \(y\). Here are a few examples:

• When \(x = 0\):

  Substituting into the equation gives:

  3(0) + 2y = 2 → 2y = 2 → y = 1

  Point: (0, 1)

• When \(x = 1\):

  Substituting into the equation gives:

  3(1) + 2y = 2 → 3 + 2y = 2 → 2y = -1 → y = -0.5

  Point: (1, -0.5)

• When \(x = -1\):

  Substituting into the equation gives:

  3(-1) + 2y = 2 → -3 + 2y = 2 → 2y = 5 → y = 2.5

  Point: (-1, 2.5)

Step 2: Plot the Points

On a graph, mark the points you calculated:

• (0, 1)
• (1, -0.5)
• (-1, 2.5)

Step 3: Draw the Line

Once you have plotted the points, use a ruler to connect them with a straight line. This line represents all the solutions to the equation \(3x + 2y = 2\).

Final Touches

Label the axes and the line if necessary. Now you have a complete graph of the equation!